Basic Suspension Transfer Function

[Iawia]

Hi All,

I am trying to obtain the transfer function Y(s)/F(s) on a basic car suspension. Attached is the page of my model but I don't believe it to be correct but I am not sure what I am doing wrong. Please Help!

Model: 2 Degrees of Freedom (Car mass 1st DOF, spring and damper fused at the bottom 2nd DOF).

I imagine this model to be simply a force being put where the fused portion of the damper and spring which should oscillate, but not according to my transfer function, so it can't be right. Typical models use a tire mass or suspension mass, but let's suppose that we simply have the chassis mass and put a force at the fused point (considered massless). I can't figure out what I'm doing wrong.

Thanks for your help. I know I can count on you guys.

-t

 

[MikeMl]

I remember doing this problem when I was a Junior in EE about 1965. It was a problem to be simulated using an ANALOG computer.

This second link might help check your equations.

 

[Iawia]

I remember doing this problem when I was a Junior in EE about 1965. It was a problem to be simulated using an ANALOG computer.

This second link might help check your equations.

Thanks for the links Mike. The second link they do use the same equation I obtained, only thing is they do not derive a transfer function as a function of the input so I am still lost.

 

[steveB]

I think what you derived is correct. If you look at your final transfer function, it basically is saying F=ma, meaning that the applied force is directly transferred through the spring and the damper to the mass. This seems correct because you don't have a mass at the point where you measure the variable x(t).

It's a little bit like pulling on a mass with a rope. An applied force is directly transmitted to the primary mass, if the mass of the rope is negligible.

But maybe you need a different transfer function, if it's not doing what you want it to do. Is force really what you want for an input?

 

[MrAl]

Hi Steve,

That's the very same thought that crossed my mind when i took a quick look at this. That's because we dont usually apply a force directly to a spring, but rather to a mass, (as we dont normally apply a current directly into an inductor) and inserting a small mass between the force and the spring might not make too much sense because the tire mass (in the direction of the force) is probably very negligible.
So in light of your thought and mine, i would vote more on distance being the desired input. This could be a distance function describing the road shape right beneath the tire (the distance being the height). After all, the force function could be very hard to determine anyway.
Note that i havent actually seen the model he wants to use yet though because i cant really make out that diagram too well so i cant comment on improvements. The one in the link provided by Mike though is more clear if he wants to work with that one. It would be nice to see a cleaner diagram of the original too.

 

[steveB]

MrAl,

I agree, I was thinking x(t) might be a good input directly, but I haven't put too much thought into it.

Those are nice references from Mike.

 

[MrAl]

Hi again Steve,


Yes i was thinking something like that too. Like a function f(x,y,t). And since y is already the height, when the tire hits the face of a rectangular rock that would generate a step change in y(t) which would move the bottom of the lower spring up to a new height and that would be the input at that point in time. So it could be a function of height ramps and pulses exciting the system. Would be cool to simulate. If i get time i will do this.
The electrical equivalent would be a pulsing (or ramping up and down) voltage source feeding an inductor (with another inductor and two capacitors and at least one resistor) similar to a wild buck circuit with no feedback.